Optimization method for polarizer and analyzer configuration and polarizing and analyzing system

Abstract

This invention discloses a method for optimizing the configuration of a polarizer and analyzer, as well as a polarizer-analyzer system. The method includes the following steps: adjusting the instrument matrix W of the polarizer and the instrument matrix A of the analyzer to minimize the equal-weighted variance EWV of the instrument matrices, thereby optimizing for Gaussian noise; and ensuring that the sum of each row of the instrument matrix W and the instrument matrix A is zero, so that the estimation variance caused by Poisson noise is independent of the sample and reaches a minimum. This invention can suppress noise to the greatest extent and make the noise pattern independent of the sample; the noise distribution pattern is the same regardless of the sample being measured.

Description

Technical Field

[0001] This invention relates to the field of polarization optical imaging technology, and in particular to a method for optimizing the configuration of a polarizer and an analyzer, as well as a polarization and analyzer system. Background Technology

[0002] Polarization imaging technology boasts advantages such as being non-invasive, non-destructive, in-situ, and capable of generating large amounts of data, leading to its widespread application in fields such as biomedicine, marine science, and atmospheric remote sensing. Based on the different forms of polarization information obtained, polarization imaging can be divided into Stokes vector measurement and Müller matrix measurement. Stokes vectors are primarily used to describe the polarization characteristics of light, while the Müller matrix characterizes the polarization features of a sample and can further extract microstructural information of the medium. This is the biggest advantage of polarization measurement compared to traditional optical measurements.

[0003] When measuring the Müller matrix, the incident light needs to be polarized and modulated, while the polarization properties of the outgoing light need to be detected to understand how the sample affects and alters the polarization characteristics of the light. Through multiple modulations and detections, the complete polarization characteristics of the sample, i.e., the sample's Müller matrix, can be obtained. In this process, the device that modulates the polarization state of the incident light is called a polarizer (PSG), and the device that detects the polarization properties of the light is called a polarizer (PSA). The structures of polarizers and analyzers are similar; their core function is to modulate the polarization state of light. A polarizer modulates natural light into polarized light with a specific polarization state; an analyzer reverses the modulation of the incident polarized light to obtain the magnitude of the incident polarized light in a specific polarization state component, and then calculates the polarization properties of the light.

[0004] The Stokes vector is a method for describing the polarization properties of light, represented as S = [S0 S1 S2 S3]. T S is a four-dimensional vector, where S0 represents the intensity of light; S1 = I0 - I 90 S² = I is the difference between the intensity components of light in the 0-degree polarization direction and the intensity components in the 90-degree polarization direction; 45 -I 135 S4 is the difference between the intensity components of light polarized at 45 degrees and 135 degrees; R -I L S0 is the difference between the intensity components of light in the right-hand polarization direction and the intensity components in the left-hand polarization direction. Normally, we only care about the polarization properties of light, so we normalize S0 to 1, and the other three components are also normalized proportionally.

[0005] A Bonga sphere is a unit sphere used to graphically describe a polarization state Stokes vector. Any polarization state can be mapped to a point on the Bonga sphere. Plotting the Stokes vector's S1, S2, and S3 as x, y, and z coordinates in a Cartesian coordinate system is the Bonga sphere representation of that Stokes vector.

[0006] The Müller matrix is ​​a transformation matrix that reflects the change in the Stokes vector of a beam of light before and after scattering.

[0007] S out =M×S in

[0008] In the formula, S out It is the Stokes vector of the emitted light, S in Here, S is the Stokes vector of the incident light, and M is the Müller matrix, a 4×4 matrix. Since CCDs (charge-coupled devices) cannot receive polarization information, only light intensity information, at least four independent polarization and analysis steps are required in actual measurements. Polarization involves incident a beam of polarized light with a known polarization state, and analysis involves calculating the polarization state S of the outgoing light through measurement. out Since the Stokes vector has four components, polarization analysis requires measuring the intensity of at least four projected components to obtain the Stokes vector of a beam of light. Thus, by measuring the output polarization state after illumination with polarized light of various different polarization states, the variation matrix of the Stokes vector, i.e., the Müller matrix, can be calculated.

[0009] Currently, polarization modulation is mainly achieved by using a polarizer and one or more phase delay devices. Multiple different polarization states are obtained by coordinating the different fast axis angles and phase delays of the phase delay devices. Therefore, it is necessary to first explain the influence of the fast axis angle and phase delay on the polarization states. The Müller matrix M of a phase delay device... δ,θ for:

[0010]

[0011] Where δ is the linear phase delay and θ is the direction of the fast axis angle.

[0012] Assume the polarization state of the incident light is S at this moment. in =[1 S1 S2 S3] T Where T represents the transpose of the matrix, i.e., for any fully polarized light, the polarization state of the emitted light can be expressed by the formula S. out =S in ×M δ,θThis means that when the same incident light (usually 0-degree linearly polarized light produced by a linear polarizer) exits from a phase retarder, we can obtain a definite polarization state. By changing the fast axis angle θ or the phase delay δ of the phase retarder, the exit polarization state will also change accordingly. Thus, by changing the phase retarder multiple times, we can obtain multiple different and known polarization states, which together form the instrument matrix W of the polarizer or the instrument matrix A of the analyzer.

[0013] Phase delay devices can be further divided into fixed phase delay devices (waveplates whose fast axis angle is changed by rotation) and electrically controlled polarizing elements (with variable phase delay). The former's main advantage is high precision, but its disadvantage is that it has moving parts and requires a rotating motor to drive the waveplate to achieve modulation of various polarization states. Therefore, the modulation speed is affected by the motor speed and is often time-consuming. The latter mainly includes liquid crystal phase delay devices (LCVR), electro-optic phase delay devices (EO), and photoelastic modulators (PEM), which change the phase delay by changing the voltage applied across them. Their main advantage is fast response speed, reaching the millisecond level. However, certain systematic errors can be caused by environmental temperature or voltage fluctuations, and the cost is relatively high. In addition, since electrically controlled polarizing elements require cable control, they are often not suitable for use with motor rotation, so their fast axis angle cannot be freely rotated during measurement.

[0014] To make the measurement of the Müller matrix more accurate and suppress noise performance, the polarizer and analyzer can be designed and optimized. Summary of the Invention

[0015] To overcome the shortcomings of the aforementioned background technology, this invention proposes an optimization method for the configuration of polarizers and analyzers, as well as a polarizer-analyzer system, to solve the problems of limited accuracy and inability to effectively suppress noise in Müller matrix measurements.

[0016] The technical problem of this invention is solved by the following technical solution:

[0017] This invention discloses a method for optimizing the configuration of a polarizer and an analyzer, comprising the following steps:

[0018] Adjust the instrument matrix W of the polarizer and the instrument matrix A of the analyzer to minimize the equal-weighted variance EWV of the polarizer and analyzer instrument matrices, thereby achieving optimization against Gaussian noise; and

[0019] The sum of each row of the instrument matrix W of the polarizer and the instrument matrix A of the analyzer is 0, so that the estimated variance caused by Poisson noise is independent of the sample and the estimated variance reaches its minimum value.

[0020] In some embodiments, the following technical solutions may also be included:

[0021] Configure the polarizer and analyzer of the measurement system so that their polarization states are pairwise orthogonal; then search for the minimum equal weighted variance (EWV) of the instrument matrices of the polarizer and analyzer; the optimal configuration is obtained when the instrument matrices of the polarizer and analyzer simultaneously satisfy the conditions of row sum being 0 and minimum EWV.

[0022] When the polarizer and analyzer are respectively a rotating polarizer and a rotating quarter-wave plate, the following relationship is satisfied for the configuration condition that makes the polarization states of the polarizer and analyzer pairwise orthogonal:

[0023]

[0024] In the formula, θ P For the first measurement, the polarizer's transmission axis direction, θ R The fast axis angular direction of the quarter-wave plate configured for the first measurement, θ P 'The transmission axis direction of the polarizer configured for the second measurement, θ R The fast axis angle of the 1 / 4 wave plate configured for the second measurement; the method adjusts the main transmission direction of the polarized light through a polarizer, and then achieves modulation of a specific polarization state through a 1 / 4 wave plate.

[0025] When the polarizer and analyzer system includes a fixed polarizer, a rotating half-wave plate, and a rotating quarter-wave plate, the following relationship is satisfied when the polarizer and analyzer are configured such that their polarization states are pairwise orthogonal:

[0026]

[0027] In the formula, θ H The fast axis angular direction of the 1 / 2 waveplate configured for the first measurement, θ R The fast axis angular direction of the quarter-wave plate configured for the first measurement, θ H 'The fast axis angular direction of the 1 / 2 waveplate configured for the second measurement, θ R 'The fast axis angle direction of the 1 / 4 wave plate configured for the second measurement;'

[0028] The modulation of the linearly polarized light direction in the method is changed from single polarizer modulation to a fixed polarizer plus a half-wave plate, which can avoid the situation where the intensity of linearly polarized light in different directions is inconsistent when the incident light is not ideal natural light, due to the rotation of the polarizer.

[0029] When the polarizer and analyzer system includes a fixed polarizer and two full-wave delay phase modulation devices, the following relationship is satisfied for the configuration condition that makes the polarization states of the polarizer and analyzer pairwise orthogonal:

[0030]

[0031]

[0032] In the formula, δ F1 This is the first measurement of the phase delay θ of the first full-wave delay phase modulator configured. F1 It is its fast axis angle, δ F2 This is the first measurement of the phase delay θ of the second full-wave delay phase modulator in the configuration. F2 It is its fast axis angle, δ F1 ' is the phase delay of the first full-wave delay phase modulator in the second measurement configuration, δ F2 ′ is the phase delay of the second full-wave delay phase modulator configured for the second measurement. The method first modulates the polarization state on the circular S1OS3 plane of the Bonga sphere using the first full-wave delay phase modulator, and then obtains the target polarization state using the second full-wave delay phase modulator.

[0033] When the polarizer and analyzer are respectively a rotating polarizer and a rotating quarter-wave plate, the optimal four-point measurement configuration of the polarizer and analyzer instruments satisfies the following relationship:

[0034]

[0035]

[0036]

[0037] In the formula, θ P For the first measurement, the polarizer's transmission axis direction, θ R The fast axis angular direction of the quarter-wave plate configured for the first measurement, θ P 'The transmission axis direction of the polarizer configured for the second measurement, θ R 'The fast axis angular direction of the 1 / 4 waveplate configured for the second measurement, θ P "The transmission axis direction of the polarizer configured for the third measurement, θ" R "The fast axis angular direction of the 1 / 4 waveplate configured for the third measurement, θ" P "'The direction of the transmission axis of the polarizer configured for the fourth measurement, θ R "' is the fast axis angular direction of the 1 / 4 wave plate configured for the fourth measurement.

[0038] When the polarizer and analyzer system includes a fixed polarizer, a rotating half-wave plate, and a rotating quarter-wave plate, the optimal four-point measurement configuration for the polarizer and analyzer satisfies the following relationship:

[0039]

[0040]

[0041]

[0042] In the formula, θ H The fast axis angular direction of the 1 / 2 waveplate configured for the first measurement, θ R The fast axis angular direction of the quarter-wave plate configured for the first measurement, θ H 'The fast axis angular direction of the 1 / 2 waveplate configured for the second measurement, θ R 'The fast axis angular direction of the 1 / 4 waveplate configured for the second measurement, θ H "The fast axis angular direction of the 1 / 2 waveplate configured for the third measurement, θ" R "The fast axis angular direction of the 1 / 4 waveplate configured for the third measurement, θ" H "'The fast axis angular direction of the 1 / 2 waveplate configured for the fourth measurement, θ R "' is the fast axis angular direction of the 1 / 4 wave plate configured for the fourth measurement.

[0043] When the polarizer and analyzer system includes a fixed polarizer and two full-wave delay phase modulation devices, the optimal four-point measurement configuration for the polarizer and analyzer satisfies the following relationship:

[0044]

[0045]

[0046]

[0047]

[0048] In the formula, δ F1 This is the first measurement of the phase delay θ of the first full-wave delay phase modulator configured. F1 It is its fast axis angle, δ F2 This is the first measurement of the phase delay θ of the second full-wave delay phase modulator in the configuration. F2 It is its fast axis angle, δ F1 ' is the phase delay of the first full-wave delay phase modulator in the second measurement configuration, δ F2 ' is the phase delay of the second full-wave delay phase modulator in the second measurement configuration, δ F1 "" is the phase delay of the first full-wave delay phase modulator in the third measurement configuration, δ F2 "This is the phase delay of the second full-wave delay phase modulator configured in the third measurement, δ" F1 "′" represents the phase delay of the first full-wave delay phase modulator configured in the fourth measurement, δ F2 "″′ is the phase delay of the second full-wave delay phase modulator configured in the fourth measurement.

[0049] When the polarizer and analyzer system includes a fixed polarizer and two half-wave delayed phase modulation devices, the optimal four-point measurement configuration for the polarizer and analyzer satisfies the following relationship:

[0050]

[0051]

[0052]

[0053]

[0054] In the formula, δ H1 δ H2 The linear phase delays θ of the two half-wave delay phase modulators configured for the first measurement are respectively. H1 θ H2 These are its fast axis angles, δ H1 ′、δ H2 δ' represents the linear phase delay of the two half-wave delay phase modulators configured for the second measurement. H1 "、δ H2 "These are the linear phase delays of the two half-wave delay phase modulators configured for the third measurement, δ" H1 "′、δ H2 "″′ represents the linear phase delay of the two half-wave delay phase modulators configured for the fourth measurement.

[0055] Furthermore, an instrument matrix is ​​formed using the polarization states represented by the actual configuration, and the instrument matrix is ​​optimized for minimum EWV using a genetic algorithm or a similar optimization algorithm. That is, a variable is set for each group, and the remaining polarization states in the group that can be explicitly represented by the variable are obtained based on the variable. Then, these polarization states will form an instrument matrix with several unknown variables. By optimizing the instrument matrix for minimum EWV using a genetic algorithm, it is possible to calculate the values ​​of these unknown variables that will minimize the EWV of the instrument matrix.

[0056] Furthermore, both the polarizer and the analyzer satisfy the modulation of the full polarization state.

[0057] The present invention also discloses a polarization detection system, comprising a rotating polarizer and a rotating quarter-wave plate, configured as follows:

[0058]

[0059] This configuration satisfies that the sum of each row of the instrument matrix W and A of the polarizer and analyzer is 0, and the EWV of the instrument matrix of the polarizer and analyzer is optimal, in order to optimize the performance of the Müller measurement system against Gaussian-Poisson mixed noise.

[0060] The present invention also discloses a polarization detection system, comprising a fixed polarizer, a rotating 1 / 2 wave plate, and a rotating 1 / 4 wave plate, configured as follows:

[0061]

[0062]

[0063] This configuration satisfies that the sum of each row of the polarizer's instrument matrix W and the analyzer's instrument matrix A is 0, and that the EWV of the polarizer and analyzer instrument matrices is optimal, in order to optimize the Müller measurement system's resistance to Gaussian-Poisson mixed noise.

[0064] The present invention also discloses a polarization detection system, comprising a fixed polarizer and two full-wave delay phase modulation devices, configured as follows:

[0065]

[0066]

[0067] This configuration satisfies that the sum of each row of the polarizer's instrument matrix W and the analyzer's instrument matrix A is 0, and that the EWV of the polarizer and analyzer instrument matrices is optimal, in order to optimize the Müller measurement system's resistance to Gaussian-Poisson mixed noise.

[0068] The present invention also discloses a polarization detection system, comprising a fixed polarizer and two half-wave delay phase modulation devices, configured as follows:

[0069]

[0070] This configuration satisfies that the sum of each row of the polarizer's instrument matrix W and the analyzer's instrument matrix A is 0, and that the EWV of the polarizer and analyzer instrument matrices is optimal, in order to optimize the Müller measurement system's resistance to Gaussian-Poisson mixed noise.

[0071] The beneficial effects of this invention compared with the prior art include: the polarizer and analyzer configuration optimization method provided by this invention, by adjusting the instrument matrix W of the polarizer and the instrument matrix A of the analyzer, minimizes the equal-weighted variance EWV of the instrument matrices of the polarizer and analyzer, thereby achieving optimization for Gaussian noise. Furthermore, the sum of each row of the instrument matrix W of the polarizer and the instrument matrix A of the analyzer is 0, making the estimation variance caused by Poisson noise independent of the sample, and minimizing the estimation variance. This achieves maximum noise suppression and makes the noise pattern independent of the sample, so that the noise distribution pattern is the same regardless of the sample being measured.

[0072] In some embodiments, this invention combines measurement configuration with optimization of Gaussian-Poisson mixed noise. By employing optimal measurement configurations of polarizers and analyzers with various different devices, the equal-weighted variance (EWV) of the polarizer and analyzer instrument matrices is minimized, further improving the performance accuracy of polarization measurements, particularly in Müller matrix measurements. This minimizes the impact of error propagation in Müller matrix measurements and makes Poisson noise independent of the sample. Furthermore, this method is universal and can be optimized for measurement systems with various structures. Attached Figure Description

[0073] Figures 1a to 1b This is a set of orthogonal polarization state diagrams formed by the rotating phase delay device in the embodiments of the present invention.

[0074] Figures 2a to 2b This is a set of orthogonal polarization state diagrams formed by the phase-variable delay device in the embodiments of the present invention.

[0075] Figure 3 This is a schematic diagram of an instrument consisting of a rotating polarizer and a rotating quarter-wave plate, as described in an embodiment of the present invention.

[0076] Figure 4 This is a schematic diagram of an instrument consisting of a fixed polarizer, a rotating 1 / 2 wave plate, and a rotating 1 / 4 wave plate, as described in an embodiment of the present invention.

[0077] Figure 5 This is a schematic diagram of an instrument consisting of a fixed polarizer and two full-wave delay phase modulation devices, as shown in an embodiment of the present invention.

[0078] Figure 6 This is a schematic diagram of an instrument consisting of a fixed polarizer and two half-wave delay phase modulation devices in an embodiment of the present invention.

[0079] Figures 7a to 7b This diagram illustrates all polarization states that can be modulated and the optimal four-point measurement framework under an instrument with a fixed polarizer and two half-wave delay phase modulation devices, as shown in this embodiment of the invention.

[0080] Figure 8 This is a flowchart of the polarizer and analyzer configuration optimization method according to an embodiment of the present invention. Detailed Implementation

[0081] The present invention will be further described below with reference to the accompanying drawings and preferred embodiments. It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other.

[0082] It should be noted that the directional terms such as left, right, up, down, top, and bottom used in this embodiment are only relative concepts or are based on the normal use of the product, and should not be considered as restrictive.

[0083] Research has shown that appropriately selecting the incident polarization state generated by the polarizer (i.e., the polarizer's instrument matrix W) and the several polarization state projection channels of the analyzer (i.e., the analyzer's instrument matrix A) can significantly improve the performance of the Müller matrix measurement system. Therefore, the optimization of this embodiment of the invention involves selecting more suitable W and A. The optimal conditions for the instrument matrices W and A are derived as follows:

[0084] Gaussian-Poisson mixed noise is often present in Müller matrix measurement systems. Evaluating the impact of noise on the variance of the Müller matrix estimation requires covariance analysis. In a Müller matrix measurement system, the relationship between the directly measured light intensity and the instrument matrix and sample Müller matrix can be expressed as:

[0085] I = A T MW

[0086] Where I is the light intensity image measured by the CCD, M is the Müller matrix of the sample, W and A represent the instrument matrices of the polarizer (PSG) and analyzer (PSA), respectively, and T represents the transpose of the matrix. For ease of calculation, the light intensity matrix and the Müller matrix of the sample are expanded into vector form using the Kronecker product:

[0087]

[0088]

[0089] Where V I and V M These are the column vector forms of the light intensity matrix I and the Müller matrix M of the sample, respectively, where -1 represents the inverse or pseudo-inverse of the matrix. According to V... M and V I The relationship between their covariance matrices can be defined as follows:

[0090]

[0091] in Represents the Kronecker integral. and V represents the column vector of the sample Müller matrix, respectively. M and the column vector V of the light intensity matrix I The relevant covariance matrix. The correct performance criterion for a Müller matrix measurement system is the sum of the variances of all elements of the Müller matrix, i.e. traces:

[0092]

[0093] The `trace()` function calculates the trace of a matrix. When additive Gaussian noise exists in the system, the covariance matrix of the light intensity noise is... It is expressed as its variance σ 2 Let be a diagonal matrix with diagonal elements. Therefore, the estimation variance of the Müller matrix caused by Gaussian noise in the system is:

[0094]

[0095] Q A =(A T A) -1 Q W =(W T W) -1 (This is a simplified form of the formula), EWV W and EWV A ...

[0096] When additive Gaussian noise exists in the system, the covariance matrix of the light intensity noise We need to utilize the properties of the Poisson distribution to give its variance from the mean of the light intensity matrix I. The diagonal elements of the matrix should be represented as:

[0097]

[0098] Where [V] M ] k Represents column vector V M The k-th element in the matrix, where i and k are both coordinate indices of the matrix. Representation matrix The value in the i-th row and i-th column, express The value of the transpose matrix at row i and column k. Using covariance analysis, the estimated variance of the Müller matrix caused by Poisson noise in the system is:

[0099]

[0100] Normalized V M Its first term is always 1. Clearly, in the above equation, the first term is independent of the sample, while the second term is related to the last 15 elements of the sample, causing the estimated variance caused by Poisson noise to change as the sample changes. Fortunately, when the EWV of the polarizer and analyzer instrument matrices is optimal, It is a constant. Therefore, when the following equation is satisfied, the second term of CPoission (C Poisson) will be set to zero, thus making the estimated variance of the Müller matrix caused by Poisson noise independent of the sample:

[0101]

[0102] The equivalent condition for the above equation is that the sum of each row of the polarizer's instrument matrix W and the analyzer's instrument matrix A is 0. When this condition is met and the EWV of the polarizer and analyzer instrument matrices is optimal, the estimation variance caused by Poisson noise is independent of the sample, and the estimation variance reaches its minimum. The optimal CPoission can then be expressed as:

[0103]

[0104] In summary, when the sum of each row of the polarizer's instrument matrix W and the analyzer's instrument matrix A is 0, and the EWV of the polarizer and analyzer instrument matrices is optimal, the Müller matrix measurement system exhibits optimal resistance to Gaussian-Poisson mixed noise. The overall system variance can be expressed as:

[0105]

[0106] So far, we have learned under what conditions the instrument matrices W and A are optimal. However, there is no direct connection between the instrument matrices at this point and the actual measurement system; we have only obtained the conditions under which the instrument matrices are optimal. Even if the instrument matrices of the actual measurement system meet the above conditions, further optimization is still needed to ensure that the actual measurement system achieves optimality. Since this optimization step aims to connect actual measurements with theory, we will use several actual measurement systems as examples to demonstrate the optimization methods and processes.

[0107] Considering the different characteristics of rotary and phase-variable delay devices, rotary devices are driven by high-precision rotary motors, resulting in smaller overall measurement errors. However, due to the slow response speed of moving parts, measurements are generally time-consuming. Electrically controlled phase-variable delay devices, on the other hand, have slightly lower accuracy due to factors such as temperature drift, but their response speed is on the order of milliseconds, enabling very fast measurements, although they are also more expensive. Therefore, the two types are rarely used interchangeably. We will optimize systems composed of these two types of phase delay devices separately. A set of orthogonal polarization states formed by a rotary phase delay device is as follows: Figures 1a to 1b As shown, a set of orthogonal polarization states formed by the phase-variable delay device are as follows: Figures 2a to 2b As shown.

[0108] This invention further improves the performance and accuracy of polarization measurements, particularly Müller matrix measurements, by employing optimal configurations of polarizers and analyzers from various different devices. It achieves an optimal configuration that minimizes the impact of error propagation in Müller matrix measurements and makes Poisson noise independent of the sample.

[0109] As mentioned earlier, the Müller matrix measurement system exhibits optimal resistance to Gaussian-Poisson mixed noise when the sum of each row of the polarizer's instrument matrix W and the analyzer's instrument matrix A is 0, and the EWV of the polarizer and analyzer instrument matrices is optimal. Therefore, if W and A of the measurement system satisfy this condition, the measurement system can naturally be optimized, achieving minimal noise transmission and independence from Poisson noise samples. However, W and A of the measurement system are determined by the polarization states generated by the polarizer and analyzer, and the polarization states generated are determined by the configuration of the measurement system (fast axis angle, phase delay, etc. of each component). Therefore, optimizing W and A is transformed into optimizing the configuration of the measurement system.

[0110] Clearly, when the polarization states of the instrument matrix are pairwise orthogonal, the last three components of the Stokes vectors of the two orthogonal polarization states are opposites of each other, and the row sum of the entire instrument matrix is ​​naturally zero, thus satisfying the first requirement of the optimal instrument matrix. In a Bonga sphere, two polarization states symmetric about the center constitute a pair of orthogonal polarization states. The instrument matrix itself is composed of multiple polarization states, and the N polarization states of the instrument matrix can form a polyhedron on the Bonga sphere. If any vertex of this polyhedron has a vertex symmetric about the center, then each polarization state also has a corresponding orthogonal polarization state. The key issue then becomes how to configure the polarizer and analyzer of the measurement system to ensure that their polarization states are pairwise orthogonal. Based on the Müller matrix M of the phase delay device… δ,θ :

[0111]

[0112] It can be seen that although we can easily calculate the polarization state of the emitted light after any polarized light passes through a phase delay device, when performing polarization state modulation, we are more concerned with what fast axis angle and phase delay relationship can satisfy the requirement of modulating the incident light into the target polarization state. In this case, the conventional forward approach cannot meet our requirements. We often need to use the fast axis angle and phase delay as input quantities and obtain the corresponding output polarization state by continuously adjusting the input, rather than designing a phase delay device that meets the requirements of the desired polarization state.

[0113] Therefore, this embodiment of the invention will first consider the influence of the properties of the phase delay device on the polarization state change from an intuitive rather than algebraic perspective. The principle can be summarized as follows:

[0114] a) When the phase delay device has a fixed fast axis angle and a linear phase delay, the trajectory of the polarization state on the Bonga sphere will be projected onto the S1 and S2 planes as a straight line.

[0115] (b) The fast axis angle of the phase retardation device determines the direction of the straight line projected onto the S1 and S2 planes by the trajectory formed by the polarization state on the Bonga sphere as the phase retardation changes with different phase delays. Furthermore, the fast axis angle θ and the angle between the projection and the S2 direction are also determined. satisfy Relationship;

[0116] c) When the phase delay device has a fixed fast axis angle and a varying linear phase delay, the trajectory of the polarization state on the Bonga sphere will form an arc. As the linear phase delay changes from 0 to 2π, the arc will become a complete circle. Simultaneously, the direction of the arc will be from the incident polarization state, forming an angle with the S2 direction. (When S3<0, it is the opposite) Draw an arc.

[0117] Further, phase delay devices can be specifically categorized into waveplates with fixed phase delay and electrically controlled components with variable phase delay (using an LCVR as an example). Waveplates are characterized by their relatively simple structure, requiring no additional control equipment, and can be easily combined with rotating motors to change the fast axis angle. However, the phase delay of a waveplate cannot be freely changed; it is usually a fixed value determined by the material of the waveplate itself. LCVRs, on the other hand, have the opposite characteristics. They have complex controllers and circuit limitations, making them unsuitable for use with moving parts. Therefore, their fast axis angle typically remains unchanged after the optical path is constructed. However, their phase delay can be easily controlled by voltage, and the electrically controlled nature results in a response speed much faster than that of a motor rotation.

[0118] Combining the characteristics of waveplates and LCVRs, we can see that LCVR devices, in practical applications, first determine a fast axis angle and then manually control and change the phase delay as needed, making them more suitable for polarization state modulation. Waveplates, on the other hand, have a fixed phase delay, and the fast axis angle is controlled by a motor, making it more difficult to achieve a satisfactory polarization state during polarization state modulation. Furthermore, due to the precision advantages of waveplates (rotating devices) and the response speed advantages of LCVRs, the two are rarely used together. Considering different costs and system requirements, we will use the following measurement optical paths with different structures as examples to illustrate the relationship that the configuration of each component (the angles of the polarizer and waveplate, and the phase delay of the electrically controlled phase-variable delayer) must satisfy during two measurements to ensure that the two resulting polarization states are orthogonal:

[0119] a) A rotating polarizer and a rotating quarter-wave plate.

[0120]

[0121] In the formula, θ P For the first measurement, the polarizer's transmission axis direction, θ R The fast axis angular direction of the quarter-wave plate configured for the first measurement, θP 'The transmission axis direction of the polarizer configured for the second measurement, θ R 'The fast axis angle direction of the 1 / 4 wave plate configured for the second measurement.'

[0122] This structure primarily adjusts the main transmission direction of the polarized light using a polarizer, and then achieves modulation of a specific polarization state using a quarter-wave plate. A schematic diagram of the instrument with a rotating polarizer and a rotating quarter-wave plate is shown below. Figure 3 As shown.

[0123] b) A fixed polarizer, a half-wave plate, and a quarter-wave plate.

[0124]

[0125] In the formula, θ H The fast axis angular direction of the 1 / 2 waveplate configured for the first measurement, θ R The fast axis angular direction of the quarter-wave plate configured for the first measurement, θ H 'The fast axis angular direction of the 1 / 2 waveplate configured for the second measurement, θ R 'The fast axis angle direction of the 1 / 4 wave plate configured for the second measurement.'

[0126] This structure is similar to the previous one, but the modulation of the linearly polarized light direction has changed from single polarizer modulation to a fixed polarizer plus a half-wave plate. This avoids the inconsistency in the intensity of linearly polarized light in different directions caused by rotating the polarizer when the incident light is not ideal natural light. A schematic diagram of the instrument consisting of a fixed polarizer, a rotating half-wave plate, and a rotating quarter-wave plate is shown below. Figure 4 As shown.

[0127] c) A fixed polarizer and two full-wave delay phase modulators.

[0128]

[0129]

[0130] In the formula, δ F1 This is the first measurement of the phase delay θ of the first full-wave delay phase modulator configured. F1 It is its fast axis angle, δ F2 This is the first measurement of the phase delay θ of the second full-wave delay phase modulator in the configuration. F2 It is its fast axis angle, δ F1 ' is the phase delay of the first full-wave delay phase modulator in the second measurement configuration, δ F2′ represents the phase delay of the second full-wave delay phase modulator in the second measurement configuration. This structure first uses the first full-wave delay phase modulator to circularly modulate the polarization state on the S1OS3 plane of the Bonga sphere, and then uses the second full-wave delay phase modulator to obtain the target polarization state. A schematic diagram of the instrument with a fixed polarizer and two full-wave delay phase modulators is shown below. Figure 5 As shown.

[0131] When the two measurement configurations satisfy the above relationship, the emitted polarization state is symmetrical on the Bonga sphere, and the sum of the S1, S2, and S3 components of the two measurements is zero, which satisfies the first condition of the optimal instrument matrix.

[0132] However, since the four polarization states modulated by this method are pairwise orthogonal during four measurements, the two sets of four modulated polarization states will form an instrument matrix with an infinite condition number, making the Müller matrix unsolvable. Therefore, the pairwise orthogonal relationship is only valid for instrument matrices with four or more points and an even number of measurements. For four points, there are only two optimal instrument matrices:

[0133]

[0134] These two instrument matrices form a regular tetrahedron on the Bonga sphere, with all three views being squares. When constraining the row sum to zero, the pairwise orthogonal approach is no longer used; instead, the constraint is based on the characteristics of the regular tetrahedron. Since all three views of the regular tetrahedron are squares, constraining the three views to ensure the four polarization states generated by the measurement system form a rectangular shape on the Bonga sphere offers a significant speed advantage over multi-point measurements. The optimal measurement framework configuration for four-point measurements is given here:

[0135] a) A rotating polarizer and a rotating quarter-wave plate.

[0136]

[0137]

[0138]

[0139] In the formula, θ P For the first measurement, the polarizer's transmission axis direction, θ R The fast axis angular direction of the quarter-wave plate configured for the first measurement, θ P 'The transmission axis direction of the polarizer configured for the second measurement, θ R 'The fast axis angular direction of the 1 / 4 waveplate configured for the second measurement, θ P "The transmission axis direction of the polarizer configured for the third measurement, θ" R"The fast axis angular direction of the 1 / 4 waveplate configured for the third measurement, θ" P "'The direction of the transmission axis of the polarizer configured for the fourth measurement, θ R "' represents the fast axis angular direction of the 1 / 4 waveplate configured for the fourth measurement. When the configuration of the four measurements satisfies the relationship given by this formula, the three views of the tetrahedron can all be rectangular.

[0140] b) A fixed polarizer, a half-wave plate, and a quarter-wave plate.

[0141]

[0142]

[0143]

[0144] In the formula, θ H The fast axis angular direction of the 1 / 2 waveplate configured for the first measurement, θ R The fast axis angular direction of the quarter-wave plate configured for the first measurement, θ H 'The fast axis angular direction of the 1 / 2 waveplate configured for the second measurement, θ R 'The fast axis angular direction of the 1 / 4 waveplate configured for the second measurement, θ H "The fast axis angular direction of the 1 / 2 waveplate configured for the third measurement, θ" R "The fast axis angular direction of the 1 / 4 waveplate configured for the third measurement, θ" H "'The fast axis angular direction of the 1 / 2 waveplate configured for the fourth measurement, θ R "' is the fast axis angular direction of the 1 / 4 wave plate configured for the fourth measurement.

[0145] c) A fixed polarizer and two full-wave delay phase modulators.

[0146]

[0147]

[0148]

[0149]

[0150] In the formula, δ F1 This is the first measurement of the phase delay θ of the first full-wave delay phase modulator configured. F1 It is its fast axis angle, δ F2 This is the first measurement of the phase delay θ of the second full-wave delay phase modulator in the configuration. F2 It is its fast axis angle, δ F1' is the phase delay of the first full-wave delay phase modulator in the second measurement configuration, δ F2 ' is the phase delay of the second full-wave delay phase modulator in the second measurement configuration, δ F1 "" is the phase delay of the first full-wave delay phase modulator in the third measurement configuration, δ F2 "This is the phase delay of the second full-wave delay phase modulator configured in the third measurement, δ" F1 "′" represents the phase delay of the first full-wave delay phase modulator configured in the fourth measurement, δ F2 "″′ is the phase delay of the second full-wave delay phase modulator configured in the fourth measurement.

[0151] d) A fixed polarizer and two half-wave delay phase modulation devices.

[0152]

[0153]

[0154]

[0155]

[0156] In the formula, δ H1 δ H2 The linear phase delays θ of the two half-wave delay phase modulators configured for the first measurement are respectively. H1 θ H2 These are its fast axis angles, δ H1 ′、δ H2 δ' represents the linear phase delay of the two half-wave delay phase modulators configured for the second measurement. H1 "、δ H2 "These are the linear phase delays of the two half-wave delay phase modulators configured for the third measurement, δ" H1 "′、δ H2 "″′ represents the linear phase delay of the two half-wave delay phase modulators configured for the fourth measurement.

[0157] This configuration cannot satisfy modulation of all polarization states, but it can satisfy the optimal framework of four points. A schematic diagram of the instrument with a fixed polarizer and two half-wave delay phase modulators is shown below. Figure 6 As shown, the instrument can modulate all polarization states and the optimal four-point measurement framework diagram are as follows. Figures 7a to 7b As shown, Figures 7a to 7bThe dark portion in the middle represents all the polarization states that can be generated by a polarizer / analyzer structure consisting of a 22.5-degree polarizer and two half-wave delay phase modulation devices (67.5 degrees and 90 degrees). The polarization states generated by this structure cannot traverse the entire Bonga sphere, but they can just cover the four polarization states of the four-point theoretically optimal instrument matrix (such as the four vertices of the light-colored regular tetrahedron).

[0158] When the above conditions are met, the four degrees of freedom of configuration can be reduced to one or two, greatly reducing the difficulty of configuration optimization. With the help of this relationship, the actual configuration of the optimal framework can be quickly obtained.

[0159] By applying the above constraints, an optimized configuration independent of Poisson noise can be obtained for both four and multiple measurements. At this point, we obtain either N / 2 sets of orthogonal polarization states (N polarization / analyzing measurements) or a set of four unknown polarization states satisfying a certain relationship (four polarization / analyzing measurements). However, we only know the internal relationship of each set, while the actual polarization states and configurations remain unknown. Therefore, we need to set a series of variables for each set and obtain the remaining polarization states in the set that can be explicitly represented by those variables. These polarization states will then form an instrument matrix with several unknown variables. The instrument matrix itself can be considered as being composed of multiple polarization states; that is, if there are four Stokes vectors S1, S2, S3, and S4, then the instrument matrix composed of these four column vectors is W = [S1 S2 S3 S4]. Whether these four Stokes vectors are completely known or represented by unknown variables, the former yields a completely known instrument matrix W, while the latter yields an instrument matrix W represented by variables. By using a genetic algorithm to optimize the instrument matrix for minimum EWV, we can calculate the values ​​of these unknown variables that will minimize the EWV of the instrument matrix. At this point, the instrument matrix and measurement configuration are clear and known, and the unknown variables have already been calculated using the algorithm.

[0160] In some embodiments, when the polarizer and analyzer are a rotating polarizer and a rotating quarter-wave plate, respectively, the process of setting a series of variables and performing EMW optimization on the variables according to their corresponding geometric constraints is as follows:

[0161] First, determine the first group of orthogonal polarization states: Let θ be the angle of the optical transmission axis of the polarizer when the first polarization state is generated in the first group of orthogonal polarization states. 1P The fast axis angle of a quarter-wave plate (hereinafter referred to as a wave plate) is θ. 1R When generating a polarization state orthogonal to it, according to the given geometric constraints, the angle of the polarizer should be θ. 1P '=θ 1P +90; the angle of the waveplate should be θ. 1R '=θ 1RTo generate an instrument matrix for eight measurements, three additional sets of orthogonal polarization states need to be generated, with polarizer and waveplate angles as follows:

[0162] θ 2P θ 2R ;θ 2P +90, θ 2R

[0163] θ 3P θ 3R ;θ 3P +90, θ 3R

[0164] θ 4P θ 4R ;θ 4P +90, θ 4R

[0165] This yields the result from θ 1P θ 1R ;θ 2P θ 2R ;θ 3P θ 3R ;θ 4P θ 4R The four sets of orthogonal polarization states are represented by eight variables. Two polarization states in each set can be represented by the corresponding variables in that set. The series of polarization states generated by these eight variables are then combined to form an instrument matrix, yielding the EWV represented by eight variables. The obtained EWV is then optimized using a genetic algorithm. While the result in this embodiment is calculated using a genetic algorithm, other optimization algorithms can also achieve this step, i.e., minimizing a result calculated from multiple variables.

[0166] The following is an example of a genetic algorithm:

[0167] This statement directly calls the ga function, which is part of MATLAB's built-in genetic algorithm. The following explains how to use this function:

[0168] [OutputVariables,EWV]=ga(@(UnknowVariables)fitfunc(UnknowVariables),8,[],[],[],[],[0 0 0 0 0 0 0 0],[180 180 180 180 180 180 180 180]);

[0169] %OutputVariables,EWV is the final output of the genetic algorithm, OutputVariables is the optimized configuration settings, and EWV is the equal-weighted variance of the instrument matrix formed by the optimized configuration.

[0170] The first input to the %ga function, fitfunc, is a target function defined by the user. Its content and definition are described in detail in lines 40-75 of the code section.

[0171] The second input of the %ga function, 8, represents the number of variables. In this example, there are 8 variables, so the input is set to 8.

[0172] The third to sixth inputs of the %ga function are some parameter settings for the genetic algorithm itself. Here, the default settings are selected, i.e., [].

[0173] The seventh input of the %ga function is the range of the minimum value of the variable. Here, all eight are set to 0, i.e., [0 0 00 0 0 0 0].

[0174] The eighth input to the %ga function is the range of the maximum value of the variable. Here, all eight are set to 180, i.e., [180 180 180 180 180 180 180 180 180].

[0175] The percentage makes the range of values ​​for all eight variables from 0 to 180 degrees.

[0176] Based on the relationship between the obtained variables and geometric constraints, calculate the remaining configurations represented by variables:

[0177] theat_R1=OutputVariables(1);

[0178] theat_P1=OutputVariables(2);

[0179] theat_P1_r = theheat_P1 + 90;

[0180] theat_R1_r = theheat_R1;

[0181] theat_R2=OutputVariables(3);

[0182] theat_P2=OutputVariables(4);

[0183] theat_P2_r = theheat_P2 + 90;

[0184] theat_R2_r = theheat_R2;

[0185] theat_R3=OutputVariables(5);

[0186] theat_P3=OutputVariables(6);

[0187] theat_P3_r = theheat_P3 + 90;

[0188] theat_R3_r = theheat_R3;

[0189] theat_R4=OutputVariables(7);

[0190] theat_P4=OutputVariables(8);

[0191] theat_P4_r = theheat_P4 + 90;

[0192] theat_R4_r = theheat_R4;

[0193] The obtained configuration and EWV will be displayed.

[0194] disp(strcat('The angles of the polarizer in the eight measurements are respectively',num2str(theat_P1),',',num2str(theat_P1_r),',',num2str(theat_P2),',',num2str(theat_P2_r),',',num2str(theat_P3),',',num2str(theat_P3_r),',',num2str(theat_P4),',',num2str(theat_P4_r)));

[0195] disp(strcat('The angles of the waveplate in the eight measurements are respectively',num2str(theat_R1),',',num2str(theat_R1_r),',',num2str(theat_R2),',',num2str(theat_R2_r),',',num2str(theat_R3),',',num2str(theat_R3_r),',',num2str(theat_R4),',',num2str(theat_R4_r)));

[0196] disp(strcat('The final EWV of the instrument matrix is',num2str(EWV)));

[0197] This function is a user-defined objective function; its inputs are variables, and its output is the value of the optimization objective.

[0198] function Fitness=fitfunc(variables)

[0199] First, some fundamental values ​​are defined, including the polarizer Müller matrix, the waveplate Müller matrix, and the incident natural light, to facilitate the calculation of Stokes:

[0200] MLR = @(x,y)[1,0,0,0;

[0201] 0,cosd(2*x)^2+sind(2*x)^2*cosd(y),cosd(2*x)*sind(2*x)*(1-cosd(y)),-sind(2*x)*sind(y);

[0202] 0,cosd(2*x)*sind(2*x)*(1-cosd(y)),sind(2*x)^2+cosd(2*x)^2*cosd(y),cosd(2*x)*sind(y);

[0203] 0,sind(2*x)*sind(y),-cosd(2*x)*sind(y),cosd(y)];% Waveplate Mueller matrix formula, x is the fast axis angle, y is the phase delay;

[0204] MLD=@(x)0.5*[1,cosd(2*x),sind(2*x),0;

[0205] cosd(2*x),cosd(2*x)^2,-cosd(2*x)*sind(2*x),0;

[0206] sind(2*x),sind(2*x)*cosd(2*x),sind(2*x)^2,0;

[0207] 0,0,0,0];% Polarizer Mueller matrix formula, x is the angle of the principal optical axis;

[0208] inputlight = [1; 0; 0; 0]; % Input is a beam of natural light without polarization.

[0209] After that, a series of Stokes are calculated.

[0210] %First group of Stokes:

[0211] Stokes1 = MLR(variables(1), 90) * MLD(variables(2)) * inputlight; % Get Stokes1 represented by the first and second variables.

[0212] Stokes1_r = MLR(variables(1),90)*MLD(variables(2)+90)*inputlight; % This gives the Stokes1_r, represented by the first and second variables and orthogonal to Stokes1. The same applies below.

[0213] %Second group of Stokes:

[0214] Stokes2=MLR(variables(3),90)*MLD(variables(4))*inputlight;

[0215] Stokes2_r=MLR(variables(3),90)*MLD(variables(4)+90)*inputlight;

[0216] %Third group of Stokes:

[0217] Stokes3=MLR(variables(5),90)*MLD(variables(6))*inputlight;

[0218] Stokes3_r=MLR(variables(5),90)*MLD(variables(6)+90)*inputlight;

[0219] % Group 4 Stokes:

[0220] Stokes4=MLR(variables(7),90)*MLD(variables(8))*inputlight;

[0221] Stokes4_r=MLR(variables(7),90)*MLD(variables(8)+90)*inputlight;

[0222] After obtaining all the Stokes, arrange them into an instrument matrix:

[0223] InstrumentMatrix=[Stokes1 Stokes1_r Stokes2 Stokes2_r Stokes3Stokes3_r Stokes4 Stokes4_r];

[0224] % Calculate the EWV of this instrument matrix:

[0225] ewv=trace((pinv(InstrumentMatrix))'*pinv(InstrumentMatrix));

[0226] The optimization objective is set as EWV.

[0227] Fitness = ewv;

[0228] end

[0229] In summary, the flowchart of the polarizer and analyzer configuration optimization method of this invention is as follows: Figure 8 As shown.

[0230] This invention systematically proposes a method for optimizing a polarization measurement system (polarizer / analyzer). The key to this method is providing a realistic and specific instrument configuration for an instrument matrix that satisfies the requirement that the estimated Poisson noise variance of the 16 array elements is independent of the sample during Müller matrix measurement. Most existing measurements do not consider Poisson noise suppression or only explain the instrument matrix required to suppress noise based on the measurement principle, without providing a configuration that can be referenced or implemented using existing devices. This invention uses the aforementioned relationship to apply geometric constraints, thereby calculating the specific instrument configuration for measurement and obtaining the corresponding configuration variations that satisfy the above relationship.

[0231] The implementation process and final results of the embodiments of the present invention are given below.

[0232] First, determine the desired measurement system structure. Except for the special structure already described above, the system, whether used as a polarizer or analyzer, must satisfy the modulation of all polarization states. Second, determine whether to optimize for four-sample or multi-sample measurements. For both cases, determine the constraints for each set of polarization states, using different polarization elements to change the polarization state pattern, and constrain each set of polarization states using the actual configuration of the measurement system. Then, form an instrument matrix from the constrained polarization states represented by the actual configuration, and use a genetic algorithm or similar optimization algorithm to perform minimum EWV optimization on this instrument matrix. This yields the optimal actual configuration.

[0233] The configurations of some polarizer and detector systems provided by the polarizer and detector configuration optimization method of this invention are as follows:

[0234] a) A rotating polarizer and a rotating quarter-wave plate.

[0235]

[0236] b) A fixed polarizer, a half-wave plate, and a quarter-wave plate.

[0237]

[0238] c) A fixed polarizer and two full-wave delay phase modulators.

[0239]

[0240]

[0241] d) A fixed polarizer and two half-wave delay phase modulation devices.

[0242]

[0243]

[0244] The configurations described in a) to d) all satisfy the condition that the sum of each row of the polarizer instrument matrix W and the analyzer instrument matrix A is 0, and that the EWV of the polarizer and analyzer instrument matrices is optimal, in order to optimize the performance of the Müller measurement system against Gaussian-Poisson mixed noise.

[0245] When using the appropriate structure for measurement, the configuration of each component needs to be set according to the parameters given in the table. For example, when using a rotating polarizer and a rotating waveplate for measurement, the first four-point configuration given in table a) can be used. That is, first, rotate the polarizer to 4.87 degrees and the waveplate to 22.5 degrees for the first polarization; then rotate the polarizer to 85.13 degrees and the waveplate to 67.5 degrees for the second polarization; then rotate the polarizer to 94.87 degrees and the waveplate to 112.5 degrees for the third polarization; finally, rotate the polarizer to 175.13 degrees and the waveplate to 157.5 degrees for the fourth polarization. Simultaneously, a polarization check is required after each polarization. The polarization check process is similar to the polarization check. Depending on the structure of the analyzer used, select the specific configuration given in the table corresponding to the structure, and perform four or eight measurements for polarization check. That is, if both polarization check and polarization check use a four-measurement mode, a total of 16 measurements are required.

[0246] Compared to traditional measurement configurations, the polarizer and analyzer configuration optimization method of this invention systematically combines measurement configuration with the optimization of Gaussian-Poisson mixed noise, providing guidance for actual measurements and enabling the measurement system to reach its optimal state. Traditional measurement systems without optimal configurations, while still capable of measurement, have limited accuracy, cannot effectively suppress noise, and exhibit unclear noise patterns, making subsequent noise reduction calculations difficult. This optimized configuration addresses these issues by minimizing noise transmission within the system and suppressing noise to the greatest extent possible. Furthermore, it ensures that the noise distribution is independent of the sample, maintaining the same pattern regardless of the sample being measured. Simultaneously, this method is universally applicable, capable of optimizing measurement systems with various structures.

[0247] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, several equivalent substitutions or obvious modifications can be made without departing from the concept of the present invention, and all such modifications, achieving the same performance or purpose, should be considered within the scope of protection of the present invention.

Claims

1. A method for optimizing the configuration of a polarizer and an analyzer, characterized in that, Includes the following steps: Adjust the instrument matrix W of the polarizer and the instrument matrix A of the analyzer to minimize the equal-weighted variance EWV of the polarizer and analyzer instrument matrices, thereby achieving optimization against Gaussian noise; and The sum of each row of the instrument matrix W of the polarizer and the instrument matrix A of the analyzer is 0, so that the estimated variance caused by Poisson noise is independent of the sample and the estimated variance reaches its minimum value. The polarizer and analyzer of the measurement system are configured such that their polarization states are pairwise orthogonal. Then, the minimum equal weighted variance (EWV) of the instrument matrices of the polarizer and analyzer is searched. When the instrument matrices of the polarizer and analyzer simultaneously satisfy the conditions of row sum being 0 and minimum EWV, the optimal configuration is obtained. When the polarizer and analyzer are respectively a rotating polarizer and a rotating quarter-wave plate, the following relationship is satisfied for the configuration condition that makes the polarization states of the polarizer and analyzer pairwise orthogonal: In the formula, The transmission axis direction of the polarizer configured for the first measurement. The fast axis angle direction of the 1 / 4 wave plate configured for the first measurement. The transmission axis direction of the polarizer configured for the second measurement. The fast axis angle of the quarter-wave plate is configured for the second measurement; the method adjusts the main transmission direction of the polarized light through a polarizer, and then achieves modulation of a specific polarization state through a quarter-wave plate; When the polarizer and analyzer system includes a fixed polarizer, a rotating half-wave plate, and a rotating quarter-wave plate, the following relationship is satisfied when the polarizer and analyzer are configured such that their polarization states are pairwise orthogonal: In the formula, The fast axis angle direction of the 1 / 2 wave plate configured for the first measurement. The fast axis angle direction of the 1 / 4 wave plate configured for the first measurement. The fast axis angle direction of the 1 / 2 waveplate configured for the second measurement. The fast axis angle direction of the 1 / 4 wave plate configured for the second measurement; The modulation of the linearly polarized light direction in the method is changed from single polarizer modulation to a fixed polarizer plus a half-wave plate, which can avoid the situation where the intensity of linearly polarized light in different directions is inconsistent when the incident light is not ideal natural light, due to the rotation of the polarizer; When the polarizer and analyzer system includes a fixed polarizer and two full-wave delay phase modulation devices, the following relationship is satisfied for the configuration condition that makes the polarization states of the polarizer and analyzer pairwise orthogonal: In the formula, This is the first measurement of the phase delay of the first full-wave delay phase modulator in the configuration. It is its fast axis angle. This is the first measurement of the phase delay of the second full-wave delay phase modulator in the configuration. It is its fast axis angle. The second measurement is of the phase delay of the first full-wave delay phase modulator in the configuration. This is the phase delay of the second full-wave delay phase modulator configured for the second measurement; the method first uses the first full-wave delay phase modulator to measure the polarization state on the Poincaré sphere. The target polarization state is obtained by circular modulation on the plane and then by using a second full-wave delay phase modulator.

2. The polarizer and analyzer configuration optimization method as described in claim 1, characterized in that, When the polarizer and analyzer are respectively a rotating polarizer and a rotating quarter-wave plate, the optimal four-point measurement configuration of the polarizer and analyzer satisfies the following relationship: In the formula, The transmission axis direction of the polarizer configured for the first measurement. The fast axis angle direction of the 1 / 4 wave plate configured for the first measurement. The transmission axis direction of the polarizer configured for the second measurement. The fast axis angle direction of the quarter-wave plate configured for the second measurement. The transmission axis direction of the polarizer configured for the third measurement. The fast axis angle direction of the quarter-wave plate configured for the third measurement. The transmission axis direction of the polarizer configured for the fourth measurement. The fast axis angular direction of the 1 / 4 wave plate configured for the fourth measurement.

3. The polarizer and analyzer configuration optimization method as described in claim 1, characterized in that, When the polarizer and analyzer system includes a fixed polarizer, a rotating 1 / 2 wave plate, and a rotating 1 / 4 wave plate, the optimal four-point measurement configuration of the polarizer and analyzer instruments satisfies the following relationship: In the formula, The fast axis angle direction of the 1 / 2 wave plate configured for the first measurement. The fast axis angle direction of the 1 / 4 wave plate configured for the first measurement. The fast axis angle direction of the 1 / 2 waveplate configured for the second measurement. The fast axis angle direction of the quarter-wave plate configured for the second measurement. The fast axis angle direction of the 1 / 2 waveplate configured for the third measurement. The fast axis angle direction of the quarter-wave plate configured for the third measurement. The fast axis angle direction of the 1 / 2 waveplate configured for the fourth measurement. The fast axis angular direction of the 1 / 4 wave plate configured for the fourth measurement.

4. The polarizer and analyzer configuration optimization method as described in claim 1, characterized in that, When the polarizer and analyzer system includes a fixed polarizer and two full-wave delay phase modulation devices, the optimal four-point measurement configuration for the polarizer and analyzer satisfies the following relationship: In the formula, This is the first measurement of the phase delay of the first full-wave delay phase modulator in the configuration. It is its fast axis angle. This is the first measurement of the phase delay of the second full-wave delay phase modulator in the configuration. It is its fast axis angle. The second measurement is of the phase delay of the first full-wave delay phase modulator in the configuration. It is the phase delay of the second full-wave delay phase modulator configured in the second measurement. This is the phase delay of the first full-wave delay phase modulator configured in the third measurement. This is the phase delay of the second full-wave delay phase modulator configured in the third measurement. This is the phase delay of the first full-wave delay phase modulator configured in the fourth measurement. It is the phase delay of the second full-wave delay phase modulator configured in the fourth measurement.

5. The polarizer and analyzer configuration optimization method as described in claim 1, characterized in that, When the polarizer and analyzer system includes a fixed polarizer and two half-wave delay phase modulation devices, the optimal four-point measurement configuration for the polarizer and analyzer satisfies the following relationship: In the formula, , The linear phase delays of the two half-wave delay phase modulators configured for the first measurement are respectively the linear phase delays of the two half-wave delay phase modulators. , These are their fast axis angles, , The linear phase delays of the two half-wave delay phase modulators configured for the second measurement are respectively... , The linear phase delays of the two half-wave delay phase modulators configured for the third measurement are respectively... , The linear phase delays of the two half-wave delay phase modulators configured for the fourth measurement are respectively.

6. The method for optimizing the configuration of the polarizer and analyzer as described in any one of claims 1-5, characterized in that, An instrument matrix is ​​formed by representing the polarization states in actual configurations. The instrument matrix is ​​then optimized for minimum EWV using a genetic algorithm or optimization algorithm. That is, a variable is set for each group, and the remaining polarization states in the group that can be explicitly represented by the variable are obtained based on the variable. Then, these polarization states will form an instrument matrix with several unknown variables. By optimizing the instrument matrix for minimum EWV using a genetic algorithm, it is possible to calculate the values ​​of these unknown variables that will minimize the EWV of the instrument matrix.

7. The method for optimizing the configuration of the polarizer and analyzer as described in any one of claims 1-4, characterized in that, Both the polarizer and the analyzer satisfy the modulation of the full polarization state.

8. A deviation detection system, characterized in that, It includes a rotating polarizer and a rotating quarter-wave plate, configured as follows: When the number of data collection points is 4, the parameters and actual configuration are as follows: = ， = ； = ， = ； = ， = ； = ， = ； or: When the number of data collection points is 4, the parameters and actual configuration are as follows: = ， = ； = ， = ； = ， = ； = ， = ； or: When the number of data collection points is 8, the parameters and actual configuration are as follows: = ， = ； = ， = ； = ， = ； = ， = ； = ， = ； = ， = ； = ， = ； = ， = ； The transmission axis direction of the polarizer configured for the first measurement. The fast axis angular direction of the 1 / 4 wave plate is configured for the first measurement; this configuration satisfies that the sum of each row of the polarizer instrument matrix W and the analyzer instrument matrix A is 0, and the EWV of the polarizer and analyzer instrument matrices is optimal, in order to optimize the performance of the Müller measurement system against Gaussian-Poisson mixed noise.

9. A deviation detection system, characterized in that, It includes a fixed polarizer, a rotated half-wave plate, and a rotated quarter-wave plate, configured as follows: When the number of data collection points is 4, the parameters and actual configuration are as follows: = ， = ， = ； = ， = ， = ； = ， = ， = ； = ， = ， = ； or: When the number of data collection points is 4, the parameters and actual configuration are as follows: = ， = ， = ； = ， = ， = ； = ， = ， = ； = ， = ， = ； or: When the number of data collection points is 8, the parameters and actual configuration are as follows: = ， = ， = ； = ， = ， = ； = ， = ， = ； = ， = ， = ； = ， = ， = ； = ， = ， = ； = ， = ， = ； = ， = ， = ； The transmission axis direction of the polarizer configured for the first measurement. The fast axis angle direction of the 1 / 2 wave plate configured for the first measurement. The fast axis angular direction of the 1 / 4 wave plate is configured for the first measurement; this configuration satisfies that the sum of each row of the polarizer instrument matrix W and the analyzer instrument matrix A is 0, and the EWV of the polarizer and analyzer instrument matrices is optimal, in order to optimize the performance of the Müller measurement system against Gaussian-Poisson mixed noise.

10. A deviation detection system, characterized in that, It includes a fixed polarizer and two full-wave delay phase modulators, configured as follows: When the number of data collection points is 4, the parameters and actual configuration are as follows: = ， = ， = ， = ， = ； = ， = ， = ， = ， = ； = ， = ， = ， = ， = ； = ， = ， = ， = ， = ； or: When the number of data collection points is 4, the parameters and actual configuration are as follows: = ， = ， = ， = ， = ； = ， = ， = ， = ， = ； = ， = ， = ， = ， = ； = ， = ， = ， = ， = ； or: When the number of data collection points is 8, the parameters and actual configuration are as follows: = ， = ， = ， = ， = ； = ， = ， = ， = ， = ； = ， = ， = ， = ， = ； = ， = ， = ， = ， = ； = ， = ， = ， = ， = ； = ， = ， = ， = ， = ； = ， = ， = ， = ， = ； = ， = ， = ， = ， = ； The transmission axis direction of the polarizer configured for the first measurement. This is the first measurement of the phase delay of the first full-wave delay phase modulator in the configuration. It is its fast axis angle. This is the first measurement of the phase delay of the second full-wave delay phase modulator in the configuration. It is its fast axis angle; this configuration satisfies that the sum of each row of the polarizer's instrument matrix W and the analyzer's instrument matrix A is 0, and the EWV of the polarizer and analyzer instrument matrices is optimal, in order to optimize the Müller measurement system's performance against Gaussian-Poisson mixed noise.

11. A deviation detection system, characterized in that, It includes a fixed polarizer and two half-wave delay phase modulators, configured as follows: When the number of data collection points is 4, the parameters and actual configuration are as follows: = ， = ， = ， = ， = ； = ， = ， = ， = ， = ； = ， = ， = ， = ， = ； = ， = ， = ， = ， = ； or: When the number of data collection points is 4, the parameters and actual configuration are as follows: = ， = ， = ， = ， = ； = ， = ， = ， = ， = ； = ， = ， = ， = ， = ； = ， = ， = ， = ， = ； The transmission axis direction of the polarizer configured for the first measurement. , The linear phase delays of the two half-wave delay phase modulators configured for the first measurement are respectively the linear phase delays of the two half-wave delay phase modulators. , These are their fast axis angles, respectively; This configuration satisfies that the sum of each row of the polarizer's instrument matrix W and the analyzer's instrument matrix A is 0, and that the EWV of the polarizer and analyzer instrument matrices is optimal, in order to optimize the Müller measurement system's resistance to Gaussian-Poisson mixed noise.

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